Question
A standing wave is produced by a wave y1 = (2.50 cm)cos(4.40 cm−1)x − (2.33 s−1)t ...
A standing wave is produced by a wave
y1 = (2.50 cm)cos(4.40 cm−1)x − (2.33 s−1)t
moving to the right, and a wave
y2 = (2.50 cm)cos(4.40 cm−1)x + (2.33 s−1)t
moving to the left. What is the smallest value on the positive
x axis for which the maximum transverse displacement of
the standing wave is equal to 2.50 cm
?
Homework Answers
Answer #1
The maximum transverse displacement of the standing wave occurs at antinode position. At the two endpoint the nodes are formed. Hence, the smallest distance on the positive x- axes for which the the maximum transverse displacement of the standing wave is equal to 2.50 cm, will be equal to one quarter of wavelength of standing wave.
If you compare the equation of standing wave to the given equation in this problem, you can obtain the value of wavelength.
where, 
is the wavelength and T is the time period and A is the amplitude.
Comparing the given equation, you can write
Therefore, the answer will be
Not the answer you're looking for?
Similar Questions
A wave on a string is described by the equation y(x,t)=3.0 cm*〖cos(〗〖2π*(x/2.4m+t/(0.2 s)))〗 . X is...
A wave on a string is described by the equation y(x,t)=3.0
cm*〖cos(〗〖2π*(x/2.4m+t/(0.2 s)))〗 . X is in meters and t is in
seconds.
Is the wave travelling to the right or to the left?
_________
What is the wave speed? _________
What is the wave frequency? __________
What is the wavelength? ___________
At t=0.50 seconds what is the displacement of the string at
x=0.20 meters. _________
Two transverse sinusoidal waves combining in a medium are described by the wave functions y1 =...
Two transverse sinusoidal waves combining in a medium are
described by the wave functions y1 = 1.00 sin π(x + 0.500t) y2 =
1.00 sin π(x − 0.500t) where x, y1, and y2 are in centimeters and t
is in seconds. Determine the maximum transverse position of an
element of the medium at the following positions. (a) x = 0.130 cm
|ymax| = ? (b) x = 0.460 cm |ymax| = ? (d) Find the three smallest
values of x...
The wave functions y1(x, t) = (0.150 m)sin(3.00x − 1.50t) and y2(x, t) = (0.250 m)cos(6.00x...
The wave functions
y1(x, t) = (0.150 m)sin(3.00x − 1.50t)
and
y2(x, t) = (0.250 m)cos(6.00x − 3.00t)
describe two waves superimposed on a string, with x and
y in meters and t in seconds. What is the
displacement y of the resultant wave at the following.
(Include the sign of the value in your answers.)
(a)
x = 0.700 m
and
t = 0
m
(b)
x = 1.15 m
and
t = 1.15 s
m
(c)
x =...
A transverse sinusoidal wave is moving along a string in the positive direction of an x...
A transverse sinusoidal wave is moving along a string in the
positive direction of an x axis with a speed of 93 m/s. At t = 0,
the string particle at x = 0 has a transverse displacement of 4.0
cm from its equilibrium position and is not moving. The maximum
transverse speed of the string particle at x = 0 is 16 m/s. (a)
What is the frequency of the wave? (b) What is the wavelength of
the wave?...
A wave on a string is described by the equation y(x, t) = 2*cos(2 π(x/4m- t...
A wave on a string is described by the equation
y(x, t) = 2*cos(2 π(x/4m- t /.1 s))
where x is in meters and t is in seconds.
a. Is the wave travelling to the right or to the left?
_________
b. What is the wave frequency? __________
c. What is the wavelength? ___________
d. What is the wave speed? _________
e. At t=0.50 seconds what is the displacement of the string at
x=0.20 meters. _________
Two waves moving in opposite directions produce a standing wave. The individual wave functions are: y1(x,...
Two waves moving in opposite directions produce a standing wave.
The individual wave functions are: y1(x, t) = 5 sin (5x – 10t)
y2(x, t) = 5 sin (5x + 10t) where x and y are in meters and t in
seconds.
A. What is the amplitude of the simple harmonic motion of the
element of the medium located at x = 5 m?
B. What is the position of the first anti-node if one end of the
string is...
A wave on a string is described by y(x,t)=( 4.0 cm )×cos[2π(x/( 1.2 m )+t/( 0.30...
A wave on a string is described by
y(x,t)=( 4.0 cm
)×cos[2π(x/( 1.2 m )+t/( 0.30 s ))] ,
where x is in m and t is in s .
Part B
What is the wave speed? v
= m/s
Part C
What is the wave frequency? f
= Hz
Part D
What is the wave length? =
m
Part E
At t = 0.75 s , what is the displacement of the string
at x = 0.10 m ? ...
A sound wave of the form s = sm cos(kx - ?t + f) travels at...
A sound wave of the form s = sm cos(kx - ?t + f) travels at 343
m/s through air in a long horizontal tube. At one instant, air
molecule A at x = 2.000 m is at its maximum positive displacement
of 6.00 nm and air molecule B at x = 2.070 m is at a positive
displacement of 2.00 nm. All the molecules between A and B are at
intermediate displacements. What is the frequency of the wave?
A standing wave on a string fixed at both ends is described by y(x,t)=2 sin((π/3)x)cos((π/3)t), where...
A standing wave on a string fixed at both ends is described by
y(x,t)=2 sin((π/3)x)cos((π/3)t), where x and y are given in cm and
time t is given in s. Answer the following questions
a) Find the two simplest travelling waves which form the above
standing wave
b) Find the amplitude, wave number, frequency, period and speed of
each wave(Include unit in the answer)
c) When the length of the string is 12 cm, calculate the distance
between the nodes...
A wave on a string has a displacement according to the equation: y(x,t) = 25.0 cm...
A wave on a string has a displacement
according to the equation:
y(x,t) = 25.0 cm sin ((36.0/m)x –
(8.00/sec)t)
Determine the amplitude, frequency,
period, velocity, and wavelength of the wave. Find the maximum x.
Also determine the transverse velocity at t = 0.16 sec and x's
maximum.
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 14 minutes ago
asked 19 minutes ago
asked 19 minutes ago
asked 26 minutes ago
asked 26 minutes ago
asked 27 minutes ago
asked 34 minutes ago
asked 45 minutes ago
asked 57 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago