/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 18 The lowest note on a grand piano... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?

Short Answer

Expert verified

The tension needed to tune the given string is2184N.

Step by step solution

01

Given information

The frequency of the lowest note on a piano is f1=27.5Hz.

The mass of the string isrole="math" localid="1650029973440" mass=400g=0.400kg.

02

Wavelength and wave speed

As the vibrating section of the string is 1.9mlong, the two ends of this vibrating wire are fixed, and the string is vibrating in the fundamental harmonic with wavelength

λ1=2L=2×1.9=3.8m

The wave speed along the string is

v=f1λ1=27.5×3.8=104.5m/s

03

Tension in the string

The linear density is given by

μ=masslength=0.4002.00=0.2kg/m

The wave speed is also given by role="math" localid="1650029766897" v=Tμ.

Substitute the given values

104.5=T0.2T=104.52×0.2=2184N

Therefore, the tension in the string is2184N.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A very thin oil film n=1.25floats on watern=1.33.

What is the thinnest film that produces a strong reflection for

green light with a wavelength of 500 nm?

FIGURE EX17.1 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s

As the captain of the scientific team sent to Planet Physics, one

of your tasks is to measure g. You have a long, thin wire labeled

1.00 g/m and a 1.25 kg weight. You have your accurate space cadet

chronometer but, unfortunately, you seem to have forgotten a

meter stick. Undeterred, you first find the midpoint of the wire by

folding it in half. You then attach one end of the wire to the wall

of your laboratory, stretch it horizontally to pass over a pulley at

the midpoint of the wire, then tie the 1.25 kg weight to the end

hanging over the pulley. By vibrating the wire, and measuring

time with your chronometer, you find that the wire’s second harmonic

frequency is 100 Hz. Next, with the 1.25 kg weight still

tied to one end of the wire, you attach the other end to the ceiling

to make a pendulum. You find that the pendulum requires 314 s to

complete 100 oscillations. Pulling out your trusty calculator, you

get to work. What value of g will you report back to headquarters?

Two in-phase speakers 2.0 m apart in a plane are emitting 1800 Hz sound waves into a room where the speed of sound is 340 m/s. Is the point 4.0 m in front of one of the speakers, perpendicular to the plane of the speakers, a point of maximum constructive interference, maximum destructive interference, or something in between?

What is the fundamental frequency of the steel wire in FIGURE P17.48?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.