Question

Two sound waves having wavelengths 81 cm and
82.5 cm produce 8 beats per second. Calculate the
speed of sound in air

Answer 1

Answer:

v=100m/s 8 beats per second

Answer 2

Given: Two sound waves having wavelengths 81 cm and 82.5 cm produce 8 beats per second

To find: the speed of sound in air

Solution: we are given a wavelength of two waves, with that first we need to find their respective frequencies

λ1 = 81cm= 0.81m, λ2 = 82.5cm= 0.825m

we know that

f=v/λ

where f is frequency, v is the speed of sound in air, λ is the wavelength

f1=v/λ1

similarly, f2=v/λ2

Now, we know that beat frequency is the difference of two frequencies of different waves that are

fb= f1 - f1

so, 8 = v/λ1 - v/λ1

8 = v[ 1//λ1 - 1/λ2 ]

on putting values we will get

v = 0.81×0.825×8/0.015

v = 356.40 m/s

Therefore, the speed of sound in the air will be v = 356.40 m/s.