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What is the wavelength if the time period of a wave is 1 millisecond and the velocity of the wave is 330m/s?
A) 33cm
B) 55cm
C) 44cm
D) 99cm

Last updated date: 01st Mar 2024
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IVSAT 2024
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Hint: Wavelengths are often defined because the distance between two successive crests or troughs of a wave. it's measured within the direction of the wave. The duration in which a wave covers a distance equal to one wavelength is called one time period. Wave speed is the distance covered by the wave per unit time. Therefore, the wavelength of the wave can be found out by using the formula $n\lambda$ =v$ \times $T

Complete step by step solution:
The following equation is understood because the wavelength formula or the wavelength equation:
 $n\lambda$ = $\dfrac{v}{f}$
 $n\lambda$ = v$ \times $T (where ' v' is that the speed of the wave and 'f' is that the frequency of the wave; T=1/f)

Thus, Wavelength of the wave = Speed of the wave/ Frequency
$ \Rightarrow $ Wavelength of the wave = Speed of the wave$ \times $time period

in this question, if the speed of a wave is 330m/s and time period of the wave is 1 millisecond therefore, the frequency of the waves is
f=$\dfrac{1}{T}$$ = \dfrac{1}{{1 \times {{10}^{ - 3}}}} = 1000Hz$
 $n\lambda$ = $\dfrac{v}{f}$
$ \Rightarrow n\lambda$ = v$ \times $T
$ \Rightarrow n\lambda$ =330$ \times $.001
$ \Rightarrow n\lambda$ =.33m

Note: Wavelength is that the distance from one crest to a different, or from one trough to a different , of a wave (which could also be an electromagnetic radiation , an acoustic wave , or the other wave). Crest is the highest point of the wave whereas the trough is the lowest. Since wavelength is distance/length, it's measured in units of lengths like metres, centimetres, millimeters, nanometres, etc.