# What is the relationship between tension and number of loops in a standing wave?

• rvhockey
In summary, a string with a frequency of 120 Hz is attached to a tuning fork and a suspended mass M, resulting in a standing wave pattern with four loops. The wavelength is 0.6m and the speed of the transverse waves along the string is 1152 m/s. To double the number of loops, the value of M should be decreased in order to decrease tension in the string. The amplitude of the standing wave is 2 cm.
rvhockey
To demonstrate standing waves, one end of a string is attached to a tuning fork with a frequency of 120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M. The value of M is such that the standing wave pattern has four "loops". The length of the string from the tuning fork to the point where the string touches the top of the pulley is 1.20 m. The linear density of the string is 1.0 x 10^-4 kg/m, and remains constant throughout the experiment.

a. Determine the wavelength of the standing wave.
b. Determine the speed of the transverse waves along the string.
c. The speed of the waves along the string increases with increasing tension in the string. Indicate whether the value of M should be increased or decreased in order to double the number of loops in the standing wave patterns. Justify your answer.
d. If a point on the string at an amplitude moves a total vertical distance of 4 cm during one complete cycle, what is the amplitude of the standing wave?

lambdan = 2L/n
fn = v/(n*2L)
v = f*lamba = sqrt(tension/(m/L)

For a, i knew since there were four loops, that it was fourth harmonic, so n=4, and 2L/4 = .6m
for b, i knew frequency was 120 Hz, and set that equal that to v/(4*2L) to get 1152 m/s.
for c, I'm a little stuck, and i know the wavelength would be smaller with a higher harmonic, and the frequency would stay the same, so the velocity would be smaller, so the tension should be smaller, but that doesn't seem right.
d was easy, amplitude is just half of the total displacement, or 2 cm.

For (c) you know that the speed of propagation is ##v=\sqrt{T/\mu}.~##You also know that ##v=\lambda f## so that $$\lambda =\frac{1}{f}\sqrt{T/\mu}.$$Should you increase or decrease ##T=Mg## to double ##\lambda## and by what factor?

## What is the 1998 AP Exam for Standing Waves?

The 1998 AP Exam for Standing Waves was a standardized exam administered by the College Board to high school students in the United States. It tested students' knowledge and understanding of standing waves, which are a type of sound or light wave that appears to be stationary due to interference.

## What topics were covered in the 1998 AP Exam for Standing Waves?

The exam covered topics such as wave properties, interference, resonance, and standing wave patterns. Students were also expected to understand the mathematical relationships between wave speed, frequency, and wavelength.

## What was the format of the 1998 AP Exam for Standing Waves?

The exam consisted of two sections: multiple-choice and free-response. The multiple-choice section had 30 questions and the free-response section had 5 questions. The exam was 90 minutes long and was scored on a scale of 1-5, with 5 being the highest score.

## How can I prepare for the 1998 AP Exam for Standing Waves?

To prepare for the exam, students should review their class notes and textbooks, as well as practice with previous AP exam questions. They can also attend review sessions or use online resources such as practice tests and study guides.

## What is the significance of the 1998 AP Exam for Standing Waves?

The 1998 AP Exam for Standing Waves is a valuable measure of students' understanding of wave properties and their ability to apply mathematical concepts to real-world situations. It also allows students to earn college credit or advanced placement in college courses, which can save both time and money in their higher education pursuits.

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