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The A string of a violin is 32 $\mathrm{cm}$ long between fixed points with a fundamental frequency of 440 $\mathrm{Hz}$ and a mass per unit length of $7.2 \times 10^{-4} \mathrm{kg} / \mathrm{m}$ . (a) What are the wave speed and tension in the string? (b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is 343 $\mathrm{m} / \mathrm{s}$ in air? (c) What is the frequency of the first over-tone of each instrument?

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Physics 101 Mechanics

Chapter 16

Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Cornell University

University of Washington

McMaster University

Lectures

08:15

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Humans can only hear sound waves as distinct pitches when the frequency lies between about 20 Hz and 20 kHz. Sound above 20 kHz is known as ultrasound and has different physical properties from sound below 20 kHz. Sound waves below 20 Hz are called infrasound. Different species have different hearing ranges. In terms of frequency, the range of ultrasound, infrasound and other upper limits is called the ultrasound.

04:49

In physics, a traveling wave is a wave that propogates without a constant shape, but rather one that changes shape as it moves. In other words, its shape changes as a function of time.

04:07

The A string of a violin i…

0:00

a. If a violin string vibr…

(a) Find the speed of wave…

03:57

02:41

04:13

A certain violin string is…

01:42

You are playing a note tha…

02:02

A string on the violin has…

03:42

02:14

03:40

(1) The A string on a viol…

02:19

A violin string $30.0 \mat…

06:04

The A string on a guitar h…

06:29

One string of a certain mu…

they're well, speed on the string and Britain is, um f is equal to me or to well, do well. And from here, we will be equal to We will be well due to f l to f l. So we can find a well speed by putting the values off FNL, which are so if and l 32 times this is the length and F we have is a 440 440 and this gives us there. The very one string is will be approximately 28 zero meter per second. So this is so this is what a In part B we are asked to find the attention in the string. So ft we can write is, um the linear density off a stream times the lost t off the speed of where we're honest re we speed on the string we already found, which is to 80. So we will make a square off this to 80. And, uh, linear mass density is given, which is 7.217 point 21 21 This is seven. Sorry. Uh, times 10 to the power minus for minus for and solving this detention we get in a string is 57 Newton's. So we have 57 Newton's. You didn't in part C. We are asked to find first order one for open pipes. So this fourth, first or doom for open pipe will be our three times or fundamental frequency. So three times a fundamental frequency we get here is ah, the value you get here is 13 20 hertz 1920 hurts End off the problem. Thank you for watching.

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