Wave On String JEE Advanced Previous Year Questions With Solutions

If a string is stretched between two horizontal poles and plucked, a simple wave is created in the string. As this wave moves through the string that portion of the string will acquire elastic energy and kinetic energy. In general, a wave in a string can be defined as the disturbance that travels through the string and transports energy and momentum. The waves in a string are transverse waves.

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Question 1) A person blows into the open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe.

(A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open

(B) a low -pressure pulse starts traveling up the pipe, if the other end of the pipe is open

(C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed

(D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed

Answer: (B) and (D)

Solution:

At the open end, the phase of the pressure wave changes by π radian due to the reflection.

At the closed end, there is no change in the phase of a pressure wave due to reflection.

Question 2) A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38⁰C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is:

(A) 14.0 cm

(B) 15.2 cm

(C) 16.4 cm

(D) 17.6 cm

Answer: (B) 15.2 cm

Solution:

e = (0.6) r = (0.6) (2) = 1.2 cm

V/4(l + e) = f

l+ e = V/4f

⇒ l = (V/4f) – e

So, (336 x 10²/4 x 512) – 1.2

= 15.2 cm

Question 3) A stationary source emits sound of frequency f₀ = 492 Hz . The sound is reflected by a large car approaching the source with a speed of 2 m/s. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz ? (Given that the speed of sound in air is 330 m/s and the car reflects the sound at the frequency it has received).

Answer: 6 Hz

Solution:

Frequency of sound as received by large cars approaching the source.

Question 4) In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from the bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is

Answer: 2200 Hz

Solution:

λ = 2(l₂ – l₁) = 2 x(24.5 – 17) = 15 cm

Now, from v = fλ

⇒ 330 = λ x 15 x 10^-2

⇒ λ = 330/(15 x 10^-2)

= 2200 Hz

Question 5) Two identical strings X and Y made of the same material have tension T_X and T_Z in them. If the fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio T_X/T_Y is

(A) 2.25

(B) 0.44

(C) 1.25

(D) 1.5

Answer: (A) 2.25

Solution:

Using

Where, T = tension

μ = mass/length

And

(T_x/T_y) = 9/4 = 2.25

Question 6) A transverse wave travels on a taut steel wire with a velocity v when tension in it is 2.06 x 10⁴ N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to

(A) 2.5 x 10⁴ N

(B) 5.15 x 10³ N

(C) 30.5 x 10⁴ N

(D) 10.2 x 10² N

Answer: (B) 5.15 x 10³ N

Solution:

The velocity of a transverse wave in a stretched wire is given by

v = √T/μ

Where,

T = tension in the wire

μ = linear density of the wire

Therefore,

= 0.515 x 10⁴ N

Question 7) A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s

(A) 12

(B) 8

(C) 6

(D) 4

Answer: (C) 6

Solution:

Length of pipe = 85 cm = 0.85 m

The frequency of oscillations of air column in closed pipe is given by

f = (2n – 1)v/ 4L

⇒ f = (2n – 1)v/ 4L ≤ 1250

⇒ [(2n – 1)x 340] /[4 x 0.85] ≤ 1250

(2n – 1) ≤ 12. 50

⇒ n ≤ 6.75 ≈ 6

Question 8) A wire of length 2L, is made by joining two wires A and B of the same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires form a node. If the number of antinodes in wire A is p and that in B is q then the ratio of p:q is

(A) 3: 5

(B) 4: 9

(C) 1: 2

(D) 1: 4

Answer: (C) 1: 2

Solution:

f_A = p/2l√(T/ρπr²)

f_B = q/2l√(T/ρπ(2r)²)

f_A = f_B

p/2l√(T/ρπr²) = q/2l√(T/ρπ(2r)²)

p/q = 1/2

Question 9) A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

(A) 2f

(B) f

(C) f/2

(D) 3f/4

Answer: (B) f

Solution:

The fundamental frequency is case (a) is f = v/2l

The fundamental frequency is case (b) is f’ = v/4(l/2)

= v/2l = f

Question 10) A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same position of the bridges. The value of M is

(A) 25 kg

(B) 5 Kg

(C) 12.5 Kg

(D) 1/25 Kg

Answer: 25 kg

Solution:

For vibrating string,

p = number of loops

f₁= f₂

5√9 = 3√M

M = (5/3)² x 9

= 25 kg

Waves on a String

Velocity of a Wave on a String

Standing Wave on a String

Power Transmitted by a Wave

Also Read:

Wave On String JEE Main Previous Year Questions With Solutions