Frequency in two different wires

In summary, to find the lowest frequency that generates a standing wave with the joint as one of the nodes, we need to calculate the velocities of the wave on the aluminum wire and the steel wire, use these velocities to calculate the wavelength, and then use the equation f = v/(wavelength) to find the frequency. At this frequency, there are two nodes present, with the joint being one of the nodes.
  • #1
LandOfStandar
61
0
I need help comprehending this one

Homework Statement



An aluminum wire. of length L1=60.0cm, cross-section area 1.00 x 10^-2 cm^2, and density 2.60g/cm^3, is joined to a steel wire, of density 7.80g/cm^3 and the same cross-section area. The compound wire, loaded with a block of mass m-10.0kg, is arranged so that the distance L2=86.6cm. Transverse waves are set up on the wire by an external source of variable frequency; a node is located at the pulley. (a) Find the lowest frequency that generates a standing wave having the joint as one of the nodes. (b) How many nodes are observed at this frequency?

Homework Equations

and

The Attempt at a Solution



f= v/(wavelength) = (n x v)/(2L)
v= (F/(linear density))

I know the F is 10.0kg x 9.80m/s^2 = 98.0N
...for the velocities do you do them saperate or together
...how do you get the wavelength
 
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  • #2
? Attempt at a Solution: To solve this problem, we need to calculate the velocity of the wave on the aluminum wire and the steel wire. We can then use this velocity to calculate the wavelength and frequency of the wave. The velocity of the wave on the aluminum wire is given by v = F/linear density, where F is the force (98N) and linear density is the mass per unit length of the wire (2.60g/cm^3). Therefore, v = 98 N / (2.60 g/cm^3) = 37.69 m/s. The velocity of the wave on the steel wire is given by v = F/linear density, where F is the force (98N) and linear density is the mass per unit length of the wire (7.80g/cm^3). Therefore, v = 98 N / (7.80 g/cm^3) = 12.56 m/s. The wavelength of the wave is given by wavelength = (2L)/n, where L is the total length of the wire (L1+L2=146.6 cm) and n is the number of nodes present in the wave. To find the lowest frequency that generates a standing wave having the joint as one of the nodes, we need to use the equation f = v/(wavelength). Therefore, f = (37.69 m/s)/((2 x 146.6 cm)/1) = 0.51 Hz. There are two nodes present at this frequency, since the joint is one of the nodes.
 

Related to Frequency in two different wires

1. What is frequency in two different wires?

Frequency in two different wires refers to the rate at which an alternating current (AC) electric signal cycles between positive and negative in two separate wires.

2. How is frequency measured in two different wires?

Frequency in two different wires is measured in Hertz (Hz), which represents the number of cycles per second.

3. What factors can affect the frequency in two different wires?

The frequency in two different wires can be affected by the voltage of the electric signal, the resistance of the wires, and the capacitance and inductance of the circuit.

4. How does frequency in two different wires impact the performance of an electrical system?

The frequency in two different wires can affect the performance of an electrical system by determining the speed at which the electric signal can be transmitted, the amount of energy that can be carried, and the stability of the system.

5. What is the relationship between frequency and wavelength in two different wires?

The frequency and wavelength in two different wires are inversely related, meaning that as the frequency increases, the wavelength decreases, and vice versa.

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