Question

a wave has a wavelength of 4.9 m and a velocity of 9.8 m/s. the medium through which this wave is traveling is then heated so that the velocity is doubled.
if the frequency remains constant, what is the wavelength of the heated wave?
2.5 m
9.8 m
14.7 m
19.6 m

Explanation:

Step1: Recall the wave - velocity formula

The formula for wave velocity is \(v = f\lambda\), where \(v\) is the velocity, \(f\) is the frequency, and \(\lambda\) is the wavelength.

Step2: Find the initial frequency

Given \(v_1=9.8\space m/s\) and \(\lambda_1 = 4.9\space m\). From \(v = f\lambda\), we can find \(f=\frac{v_1}{\lambda_1}\). Substituting the values, \(f=\frac{9.8}{4.9}=2\space Hz\).

Step3: Calculate the new velocity

The velocity is doubled, so \(v_2 = 2v_1=2\times9.8 = 19.6\space m/s\).

Step4: Find the new wavelength

Since \(f\) remains constant (\(f = 2\space Hz\)) and \(v_2=f\lambda_2\), then \(\lambda_2=\frac{v_2}{f}\). Substituting \(v_2 = 19.6\space m/s\) and \(f = 2\space Hz\), we get \(\lambda_2=\frac{19.6}{2}=9.8\space m\).

Answer:

B. 9.8 m