Question

If the frequency of a wave is increased by 25%, then the change in its wavelength is (medium not changed):

• A. \( 20\% \) increase
• B. \( 20\% \) decrease
• C. \( 25\% \) increase
• D. \( 25\% \) decrease

Hint:

When the frequency of a wave increases while the medium remains unchanged, the wavelength decreases proportionally. Use the formula \( v = f\lambda \) and apply percentage change calculations to determine the new wavelength.

Answer 1

The Correct Option is B

Step 1: Understanding the Wave Relation The relationship between the speed \( v \), frequency \( f \), and wavelength \( \lambda \) of a wave is given by the equation: \[ v = f \lambda \] Since the medium is unchanged, the wave speed \( v \) remains constant. 
Step 2: Finding the Change in Wavelength Rearranging the equation for wavelength: \[ \lambda = \frac{v}{f} \] If the frequency increases by 25\%, then the new frequency is: \[ f' = 1.25 f \] Since wave speed is constant, the new wavelength becomes: \[ \lambda' = \frac{v}{1.25 f} = \frac{\lambda}{1.25} \] 
Step 3: Calculating Percentage Change in Wavelength The percentage change in wavelength is: \[ \left( \frac{\lambda' - \lambda}{\lambda} \right) \times 100 = \left( \frac{\frac{\lambda}{1.25} - \lambda}{\lambda} \right) \times 100 \] \[ = \left( \frac{\lambda - 1.25\lambda}{1.25\lambda} \right) \times 100 \] \[ = \left( \frac{1 - 1.25}{1.25} \right) \times 100 \] \[ = \left( \frac{-0.25}{1.25} \right) \times 100 \] \[ = -20\% \] Thus, the wavelength decreases by 20%.