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$\cdot$ A 1.50 -m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 48.0 $\mathrm{m} / \mathrm{s} .$ What are the wavelength and frequency of (a) the fundamental tone? (b) the second overtone? (c) the fourth harmonic?

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(a) $\lambda_{1}=3.00 \mathrm{m} \quad-\quad f_{1}=16.0 \mathrm{Hz}$(b) $\lambda_{3}=1.00 \mathrm{m} \quad$ - $\quad f_{3}=48.0 \mathrm{Hz}$(c) $\lambda_{4}=0.750 \mathrm{m} \quad-\quad f_{4}=64.0 \mathrm{Hz}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Cornell University

University of Winnipeg

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.

03:50

A 1.50 -m-long rope is str…

03:06

03:31

15.40$\cdot$ A 1.50 -m-lon…

02:38

A 1.50-m-long rope is stre…

02:00

A $1.50-\mathrm{m}$ -long …

A string that is fixed at …

01:39

A 2-m long string is stret…

01:29

The wave velocity of a tra…

02:42

A standing wave is establi…

07:59

A string with a length of …

(a) Find the speed of wave…

01:49

A string is tied down at b…

so the velocity of the wave is 48.0 meters per second and we know that the length of the string equals 1.50 meters. So for party, when we want to find the, uh, frequency and wavelength of the fundamental, we can say that the frequency is going to be equal to the velocity divided by two times out, knowing that the wave length is going to be equal to two times the length. So this will be 48 divided by three and this is giving us 16.0 hurts. We know that Lambda one is simply going to be equal to two times the length and this will be equal to 3.0 meters for be the second overtone or the third harmonic. We get that sub three. This equals 23 times thie fundamental frequency. So this will be a 48 hertz and then for land us up three the soul of equal to two times l divided by three. So this will be 1.0 meters for part. See, we have the third rather sorry the fourth overtone. Oh, sorry. The fourth harmonic. My apologies award the third overtone and this will be f sub fort will simply be ableto four times up someone. This is equaling 64 0.0 hurts and then for the wavelength. This will simply be equal to Lambda Sub four people to two out divided by four or I'll over two or 0.75 meters. So these will be your answers for part B. C. The fundamental frequency and wavelength that stuck in overtone of frequency and wavelength and the fourth harmonic frequency and wavelength. But is the end of the solution. Thank you for watching.

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