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The wavelength of a wave is obtained by taking the ratio of wave speed and frequency.
The wavelength of the heated wave is 9.8 m. Hence, option (b) is correct.
What is frequency of a wave?
The number of oscillations completed by a wave in one second is known as the frequency of a wave. It is expressed as the ratio of the velocity of the wave to its wavelength.
Given data-
The wavelength of the wave is, [tex]\lambda = 4.9 \;\rm m[/tex].
The velocity of the wave is, v = 9.8 m/s.
The mathematical expression for the frequency of the wave is,
[tex]f = \dfrac{v}{\lambda}[/tex]
Solving as,
[tex]f = \dfrac{9.9}{4.9}\\\\f =2 \;\rm Hz[/tex]
Now, with constant frequency and the double magnitude of velocity (v' = 2 × 9.8 = 19.6 m/s). The wavelength of the heated wave is calculated as,
[tex]f = \dfrac{v'}{\lambda'}[/tex]
here,
[tex]\lambda'[/tex] is the wavelength of the heated wave.
Solving as,
[tex]2 = \dfrac{19.6}{\lambda'}\\\\\lambda' = \dfrac{19.6}{2}\\\\\lambda' = 9.8 \;\rm m[/tex]
Thus, we can conclude that the wavelength of the heated wave is 9.8 m. Hence, option (b) is correct.
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