A wave on a string is described by:
y=(3.6cm)sin(2.7x−3.1t +0.97)

where x is in meters, and t is in seconds, phase constant is in radians

Consider a particle at x= 0.50m. After
t = 0, how much time will pass before that particle first reaches its maximum transverse speed?

I tried to find the time with using the maximum transverse speed but I don't know how to find the distance

  1. 👍
  2. 👎
  3. 👁
  1. transverse speed is dy/dt, so x is constant.

    dy/dt = (3.6cm)(-3.1)cos(2.7x−3.1t +0.97)
    at x = 0.5, that is

    dy/dt = -11.16 cos(2.32-3.1t)

    To find maximum speed, you need

    y" = 11.16(-3.1) sin(2.32-3.1t) = 0
    clearly that is at 2.32-3.1t=0 or pi. t = 0.75 or 1.76
    we want a max, not a min, so t=1.76

    You can see from the graph that this is so.*0.5%E2%88%923.1t+%2B0.97)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    A string has a length of 2.50 m and is fixed at the ends. At a frequency of 85.0 Hz, a standing wave with 5 loops is formed. I got a, b and d. I need help with c and e thank you a. What is the wavelength of the waves that travel

  2. high school physics

    a string 180 cm long resonates in a standing wave that has 3 segments when driven by a 270hz vibrator. What is the speed of the waves on the string? (answer in book 324 m/s) frequency = 270 hz segments of wave = 3 v= f x wave I

  3. Physics

    Hi, can anybody provide some hints in how to approach these questions? I've been stuck on it for days!!! Thank you in advance!! Nodes of a Standing Wave: Consider a standing wave, where y represents the transverse displacement of

  4. physics(HELP)

    An unfingered guitar string is 0.73m long and is tuned to play E above middle C (330 Hz.) (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the

  1. Physics

    The speed of a transverse wave on a string is 450 m/s, while the wavelength is 0.18 m. The amplitude of the wave is 2.0 mm. What is the total up and down distance moved by the wave-particle for each cycle of the wave? What is the


    The speed of a transverse wave on a string is 450 m/s, while the wavelength is 0.18m. The amplitude of the wave is 2.0mm. How much time is required for a particle of the string to move through a total distance of 1.0km? I NEED

  3. science

    A string is waved up and down to create a wave pattern with a wavelength of 0.5 m. If the waves are generated with a frequency of 2 Hz, what is the speed of the wave that travels through the string to the other end? The speed of

  4. Earth Space Science

    the horizontal distance between a crest to the next trough of an ocean wave is 5 meters. what is the wavelength of the ocean wave? A)2 meters B)5 meters C)10 meters D)20 meters I think its 10 meters but im not so sure, I would


    The fundamental frequency of a standing wave on a 1.0 m long string is 440 Hz. What would be the wave speed of a pulse moving along the string

  2. Physics

    A transverse wave on a string is described by the following equation. y(x, t) = (0.35 m) sin[(1.25 rad/m)x + (81.2 rad/s)t] Consider the element of the string at x = 0. (a) What is the time interval between the first two instants

  3. Physics

    A string has a linear density of 6.7 x 10-3 kg/m and is under a tension of 210 N. The string is 1.6 m long, is fixed at both ends, and is vibrating in the standing wave pattern shown in the drawing. Determine the (a) speed, (b)

  4. physics

    The wave function (x,t)=(0.03m)sin(2.2x-3.5t) is for a harmonic wave on a string. (a) In what direction does this wave travel and what is its speed? (b) Find the wavelength, frequency, and period of this wave. (c) What is the

You can view more similar questions or ask a new question.