Question

As you bike toward a loudspeaker, you hear a tone with a frequency of 518 hz. Your friend who is biking away from the speaker at the same speed as you hears a tone with a frequency of 482 hz. How fast are each of you traveling?

Answer 1

The student is biking towards the loudspeaker at approximately 5 m/s, while their friend is biking away from the loudspeaker at approximately the same speed.

Step-by-step explanation:

To determine the speeds of the two bikers, we can use the concept of the Doppler effect. The frequency of the sound heard by each biker is affected by their relative motion. When the biker is moving toward the speaker, the frequency of the sound heard is higher, and when the biker is moving away from the speaker, the frequency is lower.

Using the formula for the Doppler effect, we can set up two equations:

518 Hz = ƒs * (v + VB) / (v - VA)

482 Hz = ƒs * (v - VA) / (v + VB)

Where ƒs is the frequency of the sound emitted by the loudspeaker, VA is the velocity of the biker moving toward the speaker, and VB is the velocity of the biker moving away from the speaker. v is the speed of sound, which is approximately 343 m/s.

Solving these equations, we find that the speed at which the student is biking toward the loudspeaker is approximately 5 m/s, and the speed at which their friend is biking away from the loudspeaker is also approximately 5 m/s.