Sonar systems used in water send out sound waves that reflect off the environment and then are detected. As water gets denser, the speed of sound in water increases. What would happen to the wavelength of a sonar wave as it moves into water with a 5% higher speed of sound?(1 point)

Question

Sonar systems used in water send out sound waves that reflect off the environment and then are detected. As water gets denser, the speed of sound in water increases. What would happen to the wavelength of a sonar wave as it moves into water with a 5% higher speed of sound?(1 point)
Responses

The wavelength would decrease by 5%.
The wavelength would decrease by 5%.

The wavelength would increase by 5%.
The wavelength would increase by 5%.

The wavelength would change to match the new frequency.
The wavelength would change to match the new frequency.

The wavelength would stay the same.

GPT-4o mini · Answer

The correct response is: **The wavelength would increase by 5%.** Here’s why: The speed of sound in a medium is related to the wavelength (λ) and frequency (f) of the sound wave by the equation: $$ v = f \cdot \lambda $$ where $ v $ is the speed of sound. When the speed of sound increases by 5%, keeping the frequency constant (as is typical in sonar systems), the wavelength must increase to compensate. If the speed of sound increases, the wavelength will also increase proportionally since $ \lambda = \frac{v}{f} $. Thus, the wavelength will increase accordingly with the 5% increase in speed.