What is the speed of the wave represented by y(x, t) = A sin(kx − ωt),where k = 7.0 rad/cm and ω = 3.6 rad/s?

answer should be in cm/s

I tried to subtract 7-3.6= 3.4 which is wrong and I also divided 7/3.6=1.94 , but that is wrong too. I don't know how to do this. Please help. Thanks!

do a google on

wave speed sin(kx-wt)

and there is an excellent article at unsw . edu . au

Use the equation K=w/v and solve for v.

To find the speed of the wave represented by the equation y(x, t) = A sin(kx − ωt), you need to determine the ratio between the angular frequency ω and the wave number k.

The wave number (k) represents the number of radians per unit distance or wavelength. In this case, it is given as k = 7.0 rad/cm.

The angular frequency (ω) represents the number of radians per unit time or period. In this case, it is given as ω = 3.6 rad/s.

The speed of the wave (v) can be found by dividing the angular frequency (ω) by the wave number (k):

v = ω / k

Substituting the given values:

v = 3.6 rad/s / 7.0 rad/cm

To convert the wave number from rad/cm to rad/m, multiply it by 100:

v = 3.6 rad/s / (7.0 rad/cm * 100 cm/m)

Simplifying:

v = 3.6 rad/s / 700 rad/m

Now, divide the rad/s by rad/m to get the speed in cm/s:

v = (3.6 / 700) cm/s ≈ 0.0051 cm/s

Therefore, the speed of the wave represented by the given equation is approximately 0.0051 cm/s.

To find the speed of a wave represented by the equation y(x, t) = A sin(kx − ωt), you first need to identify the variables k and ω.

In this equation, k represents the wave number and is given as 7.0 rad/cm. The wave number, k, is defined as the number of wavelengths that fit into a unit distance. In this case, it means that for every centimeter along the x-axis, there are 7 complete waves.

Similarly, ω represents the angular frequency and is given as 3.6 rad/s. The angular frequency, ω, is the rate at which the wave oscillates. It tells you how quickly the wave cycles through one complete oscillation in radians per second.

To find the speed of the wave, you can use the equation v = ω/k, where v is the velocity or speed of the wave. The angle frequency (ω) divided by the wave number (k) gives you the speed of the wave.

In this case, v = (3.6 rad/s) / (7.0 rad/cm). Since we want the speed in centimeters per second (cm/s), the unit of radians cancels out, leaving us with:

v = 3.6 / 7.0 cm/s.

Evaluating this division, the speed of the wave is approximately 0.514 cm/s.

So, the speed of the wave represented by the given equation is approximately 0.514 cm/s.

I hope this explanation helps you understand how to find the speed of a wave and how to perform the necessary calculations.