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)
the wavelength would change to match the new frequency.
the wavelength would stay the same.
the wavelength would decrease by 5%.
the wavelength would increase by 5%.

Explanation:

Step1: Recall wave formula

The relationship between wave speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) is \(v = f\lambda\). For a sonar wave, the frequency \(f\) is determined by the source (sonar system) and does not change when the wave moves into different water (same source, so \(f\) is constant).

Step2: Analyze speed and wavelength change

Given \(v = f\lambda\), and \(f\) is constant, so \(v\) and \(\lambda\) are directly proportional (\(\lambda=\frac{v}{f}\)). If the speed \(v\) increases by 5%, let the original speed be \(v_1\) and new speed be \(v_2 = 1.05v_1\). Original wavelength \(\lambda_1=\frac{v_1}{f}\), new wavelength \(\lambda_2=\frac{v_2}{f}=\frac{1.05v_1}{f}=1.05\lambda_1\). So the wavelength increases by 5%.

Answer:

The wavelength would increase by 5%. (The option: The wavelength would increase by 5%.)