Questions: Question 42 (1 point) If you increase the frequency of a wave on a string by wiggling your hand with greater frequency, what else will change? A) The wavelength will get longer. B) The wavelength will get shorter. C) The wave speed will increase. D) The wave speed will decrease.

Solution Steps

The wave speed \( v \) on a string is determined by the properties of the string (tension and linear density) and is given by the equation: \[ v = f \lambda \] where \( f \) is the frequency and \( \lambda \) is the wavelength.

When the frequency \( f \) of the wave is increased by wiggling your hand with greater frequency, the wave speed \( v \) remains constant because it depends on the properties of the string, not on the frequency. Therefore, the wavelength \( \lambda \) must adjust to maintain the constant wave speed.

Since the wave speed \( v \) is constant, increasing the frequency \( f \) will result in a decrease in the wavelength \( \lambda \) to satisfy the equation \( v = f \lambda \).

Final Answer