Question

A wave with a wavelenght of 54.0 cm is moving at 0.396 m/s. If this wave then increases its wavelenght by 1.05 cm, but maintains the same frequency, what is the new speed of the wave?

Answer 1

Let's first find the frequency of the wave from the wave speed equation:

$$v=f\lambda,$$

here, $v$ is the speed of the wave, $f$ is the frequency of the wave and $\lambda$ is the wavelength of the wave.

Then, from this equation we can find the frequency of the wave:

$$f=\dfrac{v}{\lambda}=\dfrac{0.396 \ \dfrac{m}{s}}{0.54 \ m} = 0.73 \ Hz.$$

According to the condition of the question, the wave increases its wavelenght by 1.05 cm, but maintains the same frequency:

$$\lambda_{new} = 0.54 \ m + 0.0105 \ m = 0.5505 \ m,$$ $$f_{new} = f =0.73 \ Hz.$$

Finally, we can find the new speed of the wave from the same formula:

$$v_{new}=f_{new}\lambda_{new}=0.73\ Hz\cdot 0.5505\ m=0.402 \ \dfrac{m}{s}.$$

Answer:

$v_{new}=0.402 \ \dfrac{m}{s}.$