1. (JEE Main 2022 (Online) 28th June Morning Shift)

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :

A. 282.8 ms^{$-$ 1}

B. 175.5 ms^{$-$ 1}

C. 353.6 ms^{$-$ 1}

D. 707.2 ms^{$-$ 1}

Correct Answer is Option (D)

$\frac{v}{4.08} - \frac{v}{4.16} = \frac{40}{12}$

$v = \frac{40}{12} \times \frac{4.08 \times 4.16}{0.08}$

$= 707.2$ m/s

2. (JEE Main 2022 (Online) 26th June Evening Shift)

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.

Correct Answer is 152

Given $v_{20} = 2 v_{1}$

Also $v_{20} = 4 \times 19 + v_{1}$

So $v_{20} = 152 H z$

3. (JEE Main 2021 (Online) 26th February Evening Shift)

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is field, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

A. 335 Hz

B. 345 Hz

C. 338 Hz

D. 342 Hz

Correct Answer is Option (A)

Initially beat frequency = 5Hz

so, $ρ$ _A = 340 $\pm$ 5 = 345 Hz, or 335 Hz

after filing frequency increases slightly so, new value of frequency of A > $ρ$ _A

Now, beat frequency = 2Hz

$\Rightarrow$ new $ρ$ _A = 340 $\pm$ 2 = 342 Hz, or 338 Hz

hence, original frequency of A is $ρ$ _A = 335 Hz

4. (JEE Main 2018 (Online) 16th April Morning Slot)

Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz, the original frequency of B is :

A. 430 Hz

B. 420 Hz

C. 428 Hz

D. 422 Hz

Correct Answer is Option (B)

Frequency of B, f_B = 425 $\pm$ 5 = 420 or 430 Hz

As tension of string B is increased

So, frequency of B, f_B should also increase [as f $\propto$ $\sqrt{T}$ ]

If initially f_B = 430 Hz then when f_B increases by increasing the tension then f_B $-$ f_A increases that means beat frequency increase.

So, f_B can't be 430 Hz

When f_B = 420 then when f_B increases f_A $-$ f_B decreases means beat frequency decreases. So, correct f_B = 420 Hz.

5. (JEE Main 2018 (Online) 15th April Morning Slot)

A tuning fork vibrates with frequency $256$ $H z$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $340 m s^{- 1}$ )

A. 220 cm

B. 190 cm

C. 180 cm

D. 200 cm

Correct Answer is Option (D)

The tuning fork vibrates with frequency 256 Hz and give one beat per second So, the organ pipe will have frequency (256 $\pm$ 1) Hr.

For open organ pipe,

Frequency n = $\frac{N υ}{2 ℓ}$

Here n = 255 Hz

N = 3

$υ$ = 340 m/s

$∴$ 255 = $\frac{3 \times 340}{2 \times ℓ}$

$\Rightarrow$ $ℓ$ = $\frac{3 \times 340}{2 \times 255} = 2 m$

$∴$ $ℓ$ = 2m or 200 cm

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