Question

while traveling in the same medium, sound a has a wavelength of 5 meters, while sound b has a wavelength of 10 meters. which sound will have a higher pitch? (1 point)

○ sound b, because it has a higher frequency.

○ sound b, because it has a lower frequency

○ sound a, because it has a higher frequency

○ sound a, because it has a lower frequency

Explanation:

Step1: Recall wave speed formula

In the same medium, the speed \( v \) of sound (a wave) is constant. The formula relating speed, wavelength (\( \lambda \)), and frequency (\( f \)) is \( v = \lambda f \), so \( f=\frac{v}{\lambda} \).

Step2: Compare frequencies of A and B

Given \( \lambda_A = 5 \, \text{m} \) and \( \lambda_B = 10 \, \text{m} \), and \( v \) is the same. Since \( f\propto\frac{1}{\lambda} \) (inverse proportionality when \( v \) is constant), a smaller wavelength means a higher frequency. So \( f_A=\frac{v}{5} \) and \( f_B=\frac{v}{10} \), so \( f_A > f_B \).

Step3: Relate frequency to pitch

Pitch is related to frequency: higher frequency means higher pitch. Since \( f_A > f_B \), sound A has a higher frequency, hence higher pitch.

Answer:

sound A, because it has a higher frequency