Home
NCERT Solution
Class 11
Physics
Waves
a travelling harmonic wave on a string is describe...

Question:
A travelling harmonic wave on a string is described by

y(x,t) = 7.5sin [0.0050x + 12t + π/4]

(a) What are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation?

(b) Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point at t = 2 s, 5 s and 11 s.

Answer:

(a) The given harmonic wave is:

y(x,t) = 7.5sin [0.0050x + 12t + π/4]

For x = 1 cm and t = 1s,

y = (1, 1) = 7.5sin [0.0050 + 12 + π/4]

.= 7.5sin [12.0050 + π/4]

= 7.5 sinθ

Where, θ = 12.0050 + π/4 = 12.0050 + 3.14 / 4 = 12.79 rad

= 180 /3.14 x 12.79 = 732.81°

∴ y = (1, 1) = 7.5sin [732.81°]

= 7.5 sin (90 x 8 + 12.81°)

= 7.5 sin (12.81°)

= 7.5 x 0.2217

= 1.6629 ≈ 1.663 cm

The velocity of the oscillation at a given point and time is given as:

v = d/dt y(x,t) = d/dt [7.5sin(0.0050x + 12t +π/4)]

= 7.5 x 12cos (0.0050x + 12t +π/4)

At x = 1 cm and t = 1s:

v = y(1,1) = 90 cos (12.005 + π/4)

= 90cos(732.81°) = 90cos(90 x 8 + 12.81°)

= 90cos(12.81°)

= 90 x 0.975 = 87.75 cm/s

Now, the equation of a propagating wave is given by:

y(x,t) = a sin(kx + wt + ø)

Where,

k = 2π / λ

∴ λ = 2π / k

And ω = 2πv

∴ v = ω / 2π

Speed = v = vλ = ω / k

Where

ω = 12 rad/s

k = 0.0050 m^-1

∴ v = 12 /0.0050 = 2400 cm/s

∴ Hence, the velocity of the wave oscillation at x = 1 cm and t = 1 s is not equal to the velocity of the wave propagation.

(b) Propagation constant is related to wavelength as:

k = 2π / λ

∴ λ = 2π / k = 2 x 3.14 / 0.0050

= 1256 cm = 12.56

Therefore, all the points at distances n_λ , (n =±1, ±2....and so on) i.e. ± 12.56 m, ± 25.12 m, … and so on for x = 1 cm, will have the same displacement as the x = 1 cm points at t = 2 s, 5 s, and 11 s.

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

< Previous Question

Next Question >

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='2' AND subId='8' AND ex_no!=0 AND status=1 and id!=3452 ORDER BY views desc, last_viewed_on desc limit 0,10

Popular questions of class 11 Physics

State the number of significant figures in the following:

(a) 0.007 m²

(b) 2.64 x 10²⁴ kg

(d) 6.320 J

(e) 6.032 N m^-2

(f) 0.0006032 m²

Fill in the blanks by suitable conversion of units:

(a) 1 kg m²s^–2= ....g cm²s^–2

(b) 1 m =..... ly

(d) G = 6.67 × 10^–11 N m² (kg)^–2=.... (cm)3s^–2 g^–1.

A physical quantity P is related to four observables a, b, c and d as follows :

The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

Rain is falling vertically with a speed of 30 m s^–1. A woman rides a bicycle with a speed of 10 m s^–1 in the north to south direction. What is the direction in which she should hold her umbrella?

Q: Give the magnitude and direction of the net force acting on
(a) a drop of rain falling down with a constant speed
(b) a cork of mass 10 g floating on water
(c) a kite skillfully held stationary in the sky
(d) a car moving with a constant velocity of 30 km/h on a rough road
(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.

The mass of a box measured by a grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is

(a) the total mass of the box,

(b) the difference in the masses of the pieces to correct significant figures?

On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

What amount of heat must be supplied to 2.0 x 10^-2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N² = 28; R = 8.3 J mol^-1 K^-1.)

Q: In which of the following examples of motion, can the body be considered approximately a point object:
(a) a railway carriage moving without jerks between two stations.
(b) a monkey sitting on top of a man cycling smoothly on a circular track.
(c) a spinning cricket ball that turns sharply on hitting the ground.
(d) a tumbling beaker that has slipped off the edge of a table.

A transverse harmonic wave on a string is described by

y(x,t) = 3.0 sin [36t + 0.018x + π /4]

Where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?

(b) What are its amplitude and frequency?

(d) What is the least distance between two successive crests in the wave?

SELECT ex_no,question,question_no,id,chapter FROM question_mgmt as q WHERE courseId='2' AND subId='8' AND ex_no!=0 AND status=1 and id!=3452 ORDER BY last_viewed_on desc limit 0,10

Recently Viewed Questions of Class 11 Physics

A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 x 10^-2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?

A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?

A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,

(a) during its upward motion,

(b) during its downward motion,

Do your answers change if the pebble was thrown at an angle of 45° with the horizontal direction? Ignore air resistance.

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:

(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

(b) work done by gravitational force in the above case,

(d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,

(e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.

(b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

Answer the following:

(a) You are given a thread and a metre scale. How will you estimate the diameter of the thread?

(b) A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?

(c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?

A transverse harmonic wave on a string is described by

y(x,t) = 3.0 sin [36t + 0.018x + π /4]

Where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?

(b) What are its amplitude and frequency?

(d) What is the least distance between two successive crests in the wave?

State the number of significant figures in the following:

(a) 0.007 m²

(b) 2.64 x 10²⁴ kg

(d) 6.320 J

(e) 6.032 N m^-2

(f) 0.0006032 m²

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m s^-1. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is:

(i) T, (ii) T - mv² / l , (iii) T + mv² / l , (iv) 0

T is the tension in the string. [Choose the correct alternative].

Comments

Answered by Ekta Mehta
4 months ago

Taking Screenshots on your Samsung Galaxy M31s is very easy and quick.

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

Answered by Ekta Mehta
4 months ago

Taking Screenshots on your Samsung Galaxy M31s is very easy and quick.

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

Answered by Ekta Mehta
4 months ago

Taking Screenshots on your Samsung Galaxy M31s is very easy and quick.

1
0
0
Report?

Report a problem on Specifications:

Email id:

Comments

< Previous Question

Next Question >

Popular questions of class 11 Physics

Recently Viewed Questions of Class 11 Physics

Comments

Comment(s) on this Question

Important links

Quick Links

Resources

Support