The A string of a violin is a little too tightly stretched. Beats at 4.00 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440 Hz). What is the period of the violin string oscillation?

A violinist is tuning her instrument to concert A $(440 \mathrm{~Hz})$. She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of $3 \mathrm{~Hz}$, which increases to $4 \mathrm{~Hz}$ when she tightens her violin string slightly.
(b) To get her violin perfectly tuned to concert $\mathrm{A}$, should she tighten or loosen her string from what it was when she heard the $3$-$\mathrm{Hz}$ beats?

A state trooper chases a speeder along a straight road; both vehicles move at 160 km/h. The siren on the trooper’s vehicle produces sound at a frequency of 500 Hz. What is the Doppler shift in the frequency heard by the speeder?

Find the speed of waves on a violin string of mass 800 mg and length 22.0 cm if the fundamental frequency is 920 Hz.

A sound wave of frequency 300 Hz has an intensity of 1.00 μW/m². What is the amplitude of the air oscillations caused by this wave?

Diagnostic ultrasound of frequency 4.50 MHz is used to examine tumors in soft tissue. What is the wavelength in air of such a sound wave?

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes 15 s later. If that echo were due to a single reflection off a wall opposite the door, how far from the door is the wall?

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes 15 s later. (a) If that echo were due to a single reflection off a wall opposite the door, how far from the door is the wall? (b) If, instead, the wall is 32.0 m away, how many reflections (back and forth) occur?

Graph the function. Compare to the parent graph. State the domain and range.

$$y = -5\sqrt{x}$$

Choose the correct term to complete each sentence. • combination • complement • conditional probability • dependent events • expected value • independent events • mutually exclusive • permutation • probability distribution. The predicted average outcome of many trials in an experiment is called the _____.

A telephone wire has a current of $20 \mathrm{~ \mu A}$ flowing through it. How long does it take for a charge of 15 C to pass through the wire?

A small omnidirectional stereo speaker produces waves in all directions that have an intensity of $6.50 \mathrm{~W} / \mathrm{m}^2$ at a distance of $2.50 \mathrm{~m}$ from the speaker.
(a) At what rate does this speaker produce energy?
(b) What is the intensity of this sound $7.00 \mathrm{~m}$ from the speaker?
(c) What is the total amount of energy received each second by the walls (including windows and doors) of the room in which this speaker is located?

Find the standard matrix of the linear transformation T, and use it to determine whether T is onto. $T:R^3\to R$ defined by

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}\end{pmatrix} =2x_1-5x_2+4x_3.\end{equation*}$$

Solve the equation.

$$( a - 5 ) ^ { 2 } - 4 ( a - 5 ) - 21 = 0$$