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Waves · Question 3

JEE Advanced 2025 Paper 2NumericalHard📈 Topic in 33% papers+4
1

An audio transmitter (T) and a receiver (R) are hung vertically from two identical massless strings of length 8 m with their pivots well separated along the X axis. They are pulled from the equilibrium position in opposite directions along the X axis by a small angular amplitude 0= -1(0.9) and released simultaneously. If the natural frequency of the transmitter is 660 Hz and the speed of sound in air is 330 m/s, the maximum variation in the frequency (in Hz) as measured by the receiver (Take the acceleration due to gravity g=10 m/s2) is [figure]

Answer

26 to 33

Solution

Maximum speed of each bob: v= 2gL(1- 0)= 2 10 8 0.1=4 m/s

Released from opposite sides together, they always move with equal and opposite velocities: at the mean position both approach (or both recede) at 4 m/s.

Approaching: f =660 330+4330-4=660 334326 676.2 Hz

Receding: f =660 326334 644.2 Hz

Maximum variation =f -f 32 Hz

Answer: 32

JEE Advanced 2025 Paper 2

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2

Two uniform strings of mass per unit length and 4 , and length L and 2L, respectively, are joined at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension T. If we define the frequency 0= 12L T , which of the following statement(s) is(are) correct? [figure]

  1. With a node at O, the minimum frequency of vibration of the composite string is 0.
  2. With an antinode at O, the minimum frequency of vibration of the composite string is 2 0.
  3. When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes.
  4. No vibrational mode with an antinode at O is possible for the composite string.
JEE Advanced 2024 Paper 1
3

A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed v with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be n Hz. The value of n is . [figure]

JEE Advanced 2024 Paper 1

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