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$\bullet$ A certain transverse wave is described by the equation$$y(x, t)=(6.50 \mathrm{mm}) \sin 2 \pi\left(\frac{t}{0.0360 \mathrm{s}}-\frac{x}{0.280 \mathrm{m}}\right)$$Determine this wave's (a) amplitude, (b) wavelength,(c) frequency, (d) speed of propagation, and (e) direction ofpropagation.

a) $A=6.5 \mathrm{mm}$b) $\lambda=0.280 \mathrm{m}$c) 27.77$H z$d) 7.77 $\mathrm{m} / \mathrm{s}$e) the positive $x$ direction as all the signs are similar to the general equation

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Hope College

University of Sheffield

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.

05:23

A certain transverse wave …

05:49

The wave function of a sta…

02:03

A wave on a string has a w…

07:59

04:56

The equation of a transver…

02:56

Consider the wave $y=(5 \m…

03:32

A transverse wave on a str…

01:18

The cquation of a transver…

04:30

A transverse sinusoidal wa…

01:58

A wave equation which give…

So here they're giving us an equation and they simply want the properties of the wave. We have an equation. Why of X t. So multi. Very. The equation. This legal 6.50 millimeters Time's sign of two pi of T divided by point 0360 seconds. It's and then minus X over 0.280 meters. We're going to relate this to the general equation of why of acts of anti equaling, a sign of to pie times time over a period minus X over the wavelength lambda. So for a part A. When it's asking for the amplitude, this is simply going to be 6.50 millimeters or we can convert and say 0.65 zero meters for part B. They want the wavelength. This is simply going to be what the denominator of the ex term So 0.280 meters, so that would be the wavelength and then, for part, see they're asking for the period on the frequencies of the period is point 0360 seconds, and so if the frequency will simply be equal to one over the period where one divided by 0.36 and this is giving us 27.8 hertz parte de is asking us for the velocity, so that would be simply land F. And this will be a point 28 eight times 27.8 and velocity is going to be equal to 7.78 meters per second. And then lastly, part is asking for the direction of the waves. So the waves going Toby propagating in the positive ex direction. And this is simply because of this negative term here. If this was positive, it would be moving in a negative X direction. However, because it's negative and it aligns with the general equation, we can say that this a wave is propagating in the positive ex direction. That is the end of the solution. Thank you for watching

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