# Physics wave/velocity problem

• oldunion
In summary, the speed of a wave in a stretched string is determined by the tension and the linear density of the string. By finding the wavelength and using the given equations, the maximum velocity of a particle on the string can be calculated.
oldunion
A string that is under 46.0 N of tension has linear density 5.00 g/m. A sinusoidal wave with amplitude 2.80 cm and wavelength 1.80 m travels along the string.
what is the maximum velocity of a particle on the string.

i don't know how to solve this without a frequency or length of string.

I don't recall the exact relationship, but from density and tension you can find the velocity. Since you have wavelength, you can get the frequency. I'm sure you have the relationship in your text or reference material.

From googling

c = sqrt(T/density per length)

wavelength= velocty/frequency.
and i don't understand your reference for density and tension

oldunion said:
i don't understand your reference for density and tension

The speed of a wave in a stretched string depends on the tension in the string, and on the mass of the string per unit length (kg/m) which is usually called the linear mass density. Rewriting OlderDan's formula a bit (because I don't like to use $c$ for any speed other than the speed of light, and the linear mass density is usually called $\mu$):

$$v = \sqrt {\frac {T}{\mu}}$$

Wait.. isn't this "v" the velocity of propagation? The original question asked for

what is the maximum velocity of a particle on the string.

This is the first derivative of the wave function at zero displacement, no?

Zz.

Do you understand that a "particle on the string" is moving up and down, not moving along the string with the wave?

$$v=\sqrt{\frac{T}{\mu}}$$
$$\omega=2\pi \frac{v}{\lambda}$$
$$v_{max}=\omega A$$

clive said:
$$v=\sqrt{\frac{T}{\mu}}$$
$$\omega=2\pi \frac{v}{\lambda}$$
$$v_{max}=\omega A$$

I understand the equations but why do all of them fit, why not just use the last Vmax to get the answer instead of subbing and letting the end equation be

I don't understand how getting this was the answer

Vmax = (2pi*A)/wavelength * sqrt(Tension/mu)

## 1. What is the formula for calculating wave velocity in physics?

The formula for calculating wave velocity in physics is v = λf, where v is the velocity, λ is the wavelength, and f is the frequency of the wave. This formula is known as the wave equation and is used to determine the speed at which a wave travels through a medium.

## 2. How does the medium affect the velocity of a wave?

The medium through which a wave travels can greatly affect its velocity. In general, waves travel faster through denser mediums, such as solids, and slower through less dense mediums, such as gases. Additionally, different types of waves have different velocities in the same medium.

## 3. What is the relationship between wave velocity and frequency?

The relationship between wave velocity and frequency is inverse. This means that as frequency increases, wave velocity decreases, and vice versa. This relationship is described by the wave equation, v = λf.

## 4. Can the direction of a wave affect its velocity?

Yes, the direction of a wave can affect its velocity. When a wave travels through a medium at an angle, its velocity will be different than if it was traveling in a straight line. This is known as the angle of incidence and can be calculated using principles of trigonometry.

## 5. How do you solve a physics wave/velocity problem?

To solve a physics wave/velocity problem, you will need to use the wave equation, v = λf, and plug in the given values for velocity, wavelength, and frequency. Make sure to use consistent units and solve for the unknown variable by rearranging the equation as needed. It is also important to pay attention to the direction of the wave and any other specific conditions given in the problem.

• Introductory Physics Homework Help
Replies
23
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
847
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
15
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
953
• Classical Physics
Replies
1
Views
757
• Introductory Physics Homework Help
Replies
9
Views
695
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
2K