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Question: please explain and show how to do the exercise at...

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EXAMPLE 14.11 Sour Notes Goal Apply the beat frequency concept. Problem A certain piano string is supposed to vibrate ning, what beat frequency is observed by the assistant? at a frequency of 4.40 X 102 Hz. To check its frequency, Note: Assume all numbers are accurate to two decimal a tuning fork known to vibrate at a frequency of places, necessary for this last calculation. 4.40 × 102 Hz is sounded at the same time the piano key is struck, and a beat frequency of 4 beats per second is heard. (a) Find the two possible frequencies at which the string could be vibrating. (b) Suppose the piano tuner oce ot sound and occurs it the pno s runs toward the piano, holding the vibrating tuning fork while his assistant plays the note, which is at 436 Hz. At his maximum speed, the piano tuner notices the beat fre- quency drops from 4 Hz to 2 Hz (without going through a beat frequency of zero). How fast is he moving? Use a sound speed of 343 m/s. (c) While the piano tuner is run- Strategy (a) The beat frequency is equal to the abso- lute value of the difference in frequency between the two d and occurs if the piano string is tuned either too high or too low. Solve Equation 14.20 for these two possible frequencies. (b) Moving toward the piano raises the observed piano string frequency. Solve the Doppler shift formula, Equation 14.12, for the speed of the observer. (c) The assistant observes a Doppler shift sources of souno fieuc hich is at 4Alw> the piano tuner is run for the tuning fork. Apply Equation 14.12. Solution (a) Find the two possible frequencies Case l: -i is already positive, so just drop the absolute-value signs: 五-,-五一, 4Hz = f2-4.40 × 102 Hz 444 Hz

Remarks The assistant on the piano bench and the tuner running with the fork observe different beat fre- quencies. Many physical observations depend on the state of motion of the observer, a subject discussed more fully in Chapter 26, on relativity QUESTION 14.11 Why arent beats heard when two different notes are played on the piano? EXERCISE 14.11 The assistant adjusts the tension in the same piano string, and a beat frequency of 2.00 Hz is heard when the note and the tuning fork are struck at the same time. (a) Find the two possible frequencies of the string. (b) Assume the actual string frequency is the higher frequency. If the piano tuner runs away from the piano at 4.00 m/s while holding the vibrating tuning fork, what beat frequency does he hear? (c) What beat frequency does the assistant on the bench hear? Use 343 m/s for the speed of sound. Answers (a) 438 Hz, 442 Hz (b) 3 Hz (c) 7 Hz

Please explain and show how to do the exercise (at the bottom), parts b and c. Explain what you are substituting in the Doppler equations and why. Also please explain what signs you have to use.

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