Solution Found!
Answer: A transverse wave on a string has amplitude 0.300
Chapter 15, Problem 13E(choose chapter or problem)
A transverse wave on a string has amplitude \(0.300 \mathrm{~cm}\), wavelength \(12.0 \mathrm{~cm}\), and speed \(6.00 \mathrm{~cm} / \mathrm{s}\). It is represented by \(y(x, t)\) as given in Exercise 15.12.
(a) At time \(t=0\), compute \(y\) at \(\text { 1.5-cm }\) intervals of \(x\) (that is, at \(x=0, x=1.5 \mathrm{~cm}, x=3.0 \mathrm{~cm}\), and so on) from = 0 to
= 12.0 cm. Graph the results. This is the shape of the string at time \(t=0\).
(b) Repeat the calculations for the same values \(0 x\) at times \(t=0.400 \mathrm{~s}\) and \(t=0.800 \mathrm{~s}\). Graph the shape of the string at these instants. In what direction is the wave traveling?
Equation Transcription:
Text Transcription:
0.300 cm
12.0 cm
6.00 cm/s
y(x,t)
t = 0
y
1.5-cm
x
x= 0, x=1.5 cm, x=3.0 cm
x=0 to x=12.0 cm
t = 0
o_x
t=0.400s
t=0.800s
Questions & Answers
QUESTION:
A transverse wave on a string has amplitude \(0.300 \mathrm{~cm}\), wavelength \(12.0 \mathrm{~cm}\), and speed \(6.00 \mathrm{~cm} / \mathrm{s}\). It is represented by \(y(x, t)\) as given in Exercise 15.12.
(a) At time \(t=0\), compute \(y\) at \(\text { 1.5-cm }\) intervals of \(x\) (that is, at \(x=0, x=1.5 \mathrm{~cm}, x=3.0 \mathrm{~cm}\), and so on) from = 0 to
= 12.0 cm. Graph the results. This is the shape of the string at time \(t=0\).
(b) Repeat the calculations for the same values \(0 x\) at times \(t=0.400 \mathrm{~s}\) and \(t=0.800 \mathrm{~s}\). Graph the shape of the string at these instants. In what direction is the wave traveling?
Equation Transcription:
Text Transcription:
0.300 cm
12.0 cm
6.00 cm/s
y(x,t)
t = 0
y
1.5-cm
x
x= 0, x=1.5 cm, x=3.0 cm
x=0 to x=12.0 cm
t = 0
o_x
t=0.400s
t=0.800s
ANSWER:
Solution 13E
The wave function for a sinusoidal wave is given as,
Given, amplitude
Wavelength
At time t = 0 s,
…..(1) since , t = 0
Now, x intervals is given to be 1.5.
Therefore, various x values starting from x = 0 will be x = 12.0 cm are,
0, 1.5, 3, 4.5, 6, 7.5, 9, 10.5 and 12
Substituting these values of x in equation (1), we get
Similarly,
The graph of y(x) vs x is done as shown below.
x |
y(x) cm |
0 |
0.3 |
1.5 |
0.21 |
3 |
0 |
4.5 |
-0.21 |
6 |
-0.3 |
7.5 |