Establish the relationship between speed of sound, its wavelength and frequency. If velocity of sound in air is `340 m//s`, calculate :
(i) wavelength when frequency is `256 Hz`.
(ii) frequency when wavelength is `0.85 m`.

Answer

` lambda= 1.33 m`
` v =400 Hz`

Explanation

The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit time.
We know that, speed (v) `=("distance")/("time")=(lambda)/(T)`
Here, `lambda` is the wavelength of the sound wave. It is the distance travelled by the sound wave in one time period (T) of the wave
`v=(lambda)/(T)=lambdaxx(1)/(T)`
We know that, `v=(1)/(T)" "`(Where v=frequency)
i.e., `" "` Speed=wavelength `xx` frequency
Given, speed of sound in air v=340 m/s and frequency v=256 Hz.
(i) `therefore " "` Speed = wavelength `xx` frequency
`implies 340=lambda xx 256`
`implies lambda=(340)/(256)= 1.33 m`
(ii) Again, given
wavelength `lambda=0.85m`
Then, frequency of sound in air , `v=("speed")/("wavelength")" "` (`because` speed=wavelength `xx` frequency)
`implies " "v=(340)/(0.85)=(340xx100)/(85)=400 Hz`
Thus, frequency of sound is 400 Hz.