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# Problem_Set_2answers.pdf

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McMaster University

Psychology

PSYCH 3A03

Paul Faure

Fall

Description

Psych 3A03 20 September 2013
McMaster University Paul A. Faure
Instructions and Tips
-1
• The speed of sound in air (c ) air= 340 m⋅s ; the speed of sound in water (c water is = 4⋅air
• Remember that log (2)10 0.3.
• A calculator is not necessary to answer any of these questions.
1. Write the equation for a line with a slope of 1, 3 and 5, each having a y -intercept equal to its slope.
(a) Line 1: y = 1⋅x + 1
(b) Line 2: y = 3⋅x + 3
(c) Line 2: y = 5⋅x + 5
2. Draw the unit circle andlabelpointsatevery
π/4 radians starting from x=1, y=0. What angle
(θ) in degrees corresponds to each π/4 radian
point starting from x=1, y=0?
Angles are every 45°.
θ = 45°, 90°, 135°, 180°, 225°, 270°, 315°, 360°
starting from the reference point x=1, y=0.
3. (a) Write the equation that describes the instantaneous pressure, P(t) , of a sine wave with a peak
amplitude of 4 Pascals (Pa), a period (T) of 1 ms, and a starting phase angle (θ) of 3.14 radians (rad).
A = 4 Pa; T = 1 ms = 0.001 s; f = 1/T ; f = 1/ 0.001 ; f = 1000/1 ; ∴ f = 1000 Hz ; θ = 3.14 rad = 180° = π
P(t) = 4⋅sin(2π⋅1000⋅t + π)
(b) Write the equation for the instantaneous pressure of the above sound if the frequency (f) is doubled
and the starting phase angle (θ) is shifted by -90°.
IF f = 1000 Hz in 3(a), THEN f = 2000 Hz in 3(b) ; θ = 180° – 90° = 90° = π/2
P(t) = 4⋅sin(2π⋅2000⋅t + π/2)
(c) Write the equation that describes the instantaneous pressure, P(t) , of a sine wave with a peak
amplitude of 0.01 Pa, a frequency (f) of 5000 Hz, and a starting phase angle (θ) of 270°.
A = 0.01 Pa ; f = 5000 Hz ; θ = 270° = 3/2⋅π or -1/2⋅π
P(t) = 0.01⋅sin(2π⋅5000⋅t + 3/2⋅π) or P(t) = 0.01⋅sin(2π⋅5000⋅t - 1/2⋅π)
Problem Set #2 page 1 of 3 Psych 3A03 20 September 2013
McMaster University Paul A. Faure
4. What is the period (T) of a sine wave with a frequency (f) of:
(a) 10 Hz? T = 0.1 s (or 100 ms) (e) 1000 Hz? T = 0.001 s (or 1 ms)
(b) 100 Hz? T = 0.01 s (or 10 ms) (f) 2 kHz? T = 0.0005 s (or 0.5 ms)
(c) 333 Hz? T = 0.003 s (or 3 ms) (g) 5 kHz? T = 0.0002 s (or 0.2 ms)
(d) 500 Hz? T = 0.002 s (or 2 ms) (h) 10 kHz? T = 0.0001

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