A musical tone's pitch varies inversely with its wavelength. If one tone has a pitch of 420 vibrations each second and a wavelength of 2.1 meters, find the wavelength of a tone that has a pitch of 690 vibrations each second. Please round your answer to the nearest hundredth.
A) 0.01 meters
B) 0.78 meters
C) 1.28 meters
D) 4.42 meters
E) 3.45 meters

Question

Quizplus · Accepted Answer

Use the formula $v=f\lambda$, where $v$ is the speed of sound (which we can assume is constant), $f$ is the frequency, and $\lambda$ is the wavelength. Rearranging, we get $\lambda=\frac{v}{f}$. Plugging in the values for the first tone, we get $\lambda_1=\frac{v}{f_1}=\frac{v}{420}$. To find the wavelength of the second tone, we set the two equations equal to each other and solve for $\lambda_2$: $$\frac{v}{420}=\frac{v}{690}\lambda_2$$ $$\lambda_2=\frac{420}{690}\approx\boxed{1.28}$$. meters. The answer is (C).

A Musical Tone's Pitch Varies Inversely with Its Wavelength