Write a relation between wavelength (lam...

Write a relation between wavelength `(lambda)` , frequency (upsilon)` and speed of wave (c).

Text Solution

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1) Speed of sound can be defined as the distance by which a point on the wave, such as a compression or rarefaction, travels in unit time.
2) Let the distance travelled by a wave in T seconds `= lambda` meters
3) The distance travelled by a wave in 1 seconds `= (lambda)/(T)` meters
Thus by definition of speed of wave, `v = (lambda)/(T)" " " ""............."(1)`
5) We know that frequency and time period are related as `upsilon = (1)/(T)" " " "".............."(2)`
6) From (1) and (2) we get `v = lambda. upsilon`
Speed of sound = Frequency `xx` Wavelength.

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The graph between wave number (1) and angular frequency (0) is

A trnsvese sinusoidal wave of amplitude a, wavelength lambda , and. frequency f is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If a = 10^(-3) m and v = 10 m/s, then lambda and f are given by

`lambda = 2pi xx 10^(-2) m`

`lambda = 10^(-3)` m

`f = 10^(3)/(2pi)Hz`

`f = 10^(4) Hz`

A transverse sinusoidal wave of amplitude a, wavelength lamda and frequency f is travelling on a stretched string. The maximum speed of any point on the string is v/10, where v is the speed of propagation of the wave. If a = 10^(-3) m and y = 10m/s, then lamda and f are given by

`lamda = 2pi xx 10^(-2) m`

`lamda = 10^(-3) m`

`f = (10^3)/(2pi) Hz `

`f = 10^4 Hz `