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Question

Physics Question on Waves

Two waves of wavelengths 50 cm and 51 cm produced 12 beats per sec. The velocity of sound is

A

340 m s−1{ 340 \, m \, s^{-1}}

B

331 m s−1{ 331\, m \, s^{-1}}

C

306 m s−1{ 306 \, m \, s^{-1}}

D

360 m s−1{ 360\, m \, s^{-1}}

Answer

306 m s−1{ 306 \, m \, s^{-1}}

Explanation

Solution

Number of beats produced per second
=υ1−υ2=υλ1−υλ2= \upsilon_1 - \upsilon_2 = \frac{\upsilon}{\lambda_1} - \frac{\upsilon}{\lambda_2}
12=υ[150−151]12 = \upsilon \left[ \frac{1}{50} - \frac{1}{51} \right] or 12=υ×150×5112 = \frac{ \upsilon \times 1}{50 \times 51}
or, υ=12×50×51cm s−1=306 m s−1\upsilon = 12 \times 50 \times 51 { cm \, s^{-1} = 306 \, m \, s^{-1}}