set5-soln - Physics 1240 Homework 5 solutions Brief...

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Physics 1240 Homework 5 solutions Brief solutions to homework set #5. Your numbers will be different, but the idea is the same. I’m just using sample numbers here. 1. String instrument players can tune one string off of another— once you are happy with the tension and resulting pitch in one lower string, you put your finger down partway up the first string at the appropriate spot to make a higher pitch, one which should match the fundamental pitch of the next string over. If the second string is almost, but not quite properly tuned, you will hear beats. Suppose you are doing this, and hear one beat every 1.12 s when trying to adjust the second string. If the first string (with your finger on it) is playing at 107 Hz how far off in frequency is the second string? Note that this frequency for the first string might not match a standard guitar, perhaps it’s a more unusual string instrument! What does this “beating” actually sound like? Describe it in your own words, as clearly as you can. What note are you hearing? What does it sound like as time goes by? If you wanted the two strings to be tuned exactly, how could you use the phenomenon of beats to help you? What exactly would you do to help you tune the instrument? Because there is one beat every 1.12 s, the period of the beats is P = 1 . 12 s. The beat frequency is f = 1 /P = 0 . 893 Hz. Since the beat frequency is equal to the difference in frequency of the two strings, the second string is about 0.893 Hz off in frequency. Listening to these beats sounds like hearing a note with frequency of 107 Hz, which gradually gets louder and softer and louder and softer. The time to go from when it’s most loud, to most
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