Projectile motion - 1 VCE Physics.com The decibel scale

• Sound intensity • Sound level: The decibel scale • Sound level calculations • Some decibel measurements • Change in intensity • Human hearing • The Phon scale

The decibel scale - 2 VCE Physics.com Sound intensity

• The intensity of sound decreases with the square of the distance from the source.

power P 2 Sound intensity = I = (unit =W /m ) area A

 2 P I2 r1 I = =  2 I r 4πr 1  2 

The decibel scale - 3 VCE Physics.com Sound intensity

• eg a sound source emitting a power of 1 mW, when heard at a distance of 1 vs 2 m

P 1×10−3W I = = = 8×10−5W /m2 A 4π 1m 2 ( ) P 1×10−3W I = = =2×10−5W /m2 A 4π 2m 2 ( )

The decibel scale - 4 VCE Physics.com Sound level: The decibel scale

• The decibel scale is a relative scale, based upon the threshold of -12 2 hearing I0 = 10 W/m . • It is a logarithmic scale, an increase of 10 corresponds to 10 times the intensity. • 20dB = 102 times, 30dB = 103 times the intensity.

I L =10log I0  L   −12 10  2 I =10 W /m I L =10log −12 10

The decibel scale - 5 VCE Physics.com Sound level calculations

• eg A sound has the intensity of 10-4 W/m2. This is a sound level of

−4 I 10 8 L =10log =10log −12 =10log10 = 80dB I0 10

eg The intensity of a 45 dB sound is

 L  45   −12  −12 10  10  −7.5 −8 2 I =10 =10 =10 =3.2×10 W /m

What is the intensity of 120 dB?

 L  120   −12  −12 10   10  0 2 I =10 =10 =10 =1W /m

The decibel scale - 6 VCE Physics.com Some decibel measurements

Source Intensity (W/m2) Sound level (dB) Threshold of hearing 10-12 0 dB Soft whisper 10-10 20 dB Quiet conversation 10-8 40 dB Loud conversation 10-6 60 dB Highway traffic 10-4 80 dB Tractor engine 10-2 100 dB Threshold of pain (Rock concert) 10-0 (1) 120 dB Jet engine (less than 50 m away) 102 (100) 140 dB Rocket launch (less than 500 m away) 104 (10,000) 160 dB +

• Damage to hearing is due to both the sound level & exposure time. • The biggest risk to hearing loss for most young people today is loud headphones!

The decibel scale - 7 VCE Physics.com Change in intensity

I2 I1 ΔL =L2 −L1 =10log −10log I0 I0 I ΔL =10log 2 I1 Double intensity: ΔL =10log2≈ +3dB 1 Half intensity: ΔL =10log =−10log2≈ −3dB 2

Doubling the distance from a source gives one quarter of the intensity: 1 ΔL =10log =−10log4 ≈ −6dB 4

The decibel scale - 8 VCE Physics.com Human Hearing

• The human ear can hear sounds from ~20 Hz → 20 kHz • Our ears are most responsive to frequencies ~2-3 kHz • As we age, we lose sensitivity to the higher frequencies. • The dBA & Phon scales is weighted so that a reading is of equal perceived loudness regardless of frequency.

The decibel scale - 9 VCE Physics.com The phon scale

• The phon scale shows how human ears respond to sounds at different frequencies. • Different frequencies at the same Phon level are perceived to be equally loud. • Based on the perception of 1kHz at different intensities. • Sounds at 2 - 3 kHz are generally the loudest to our ears. • At higher intensities, the dB differences between perceived equally loud sounds are less.

The decibel scale - 10 VCE Physics.com The phon scale 120 Phon 110 Phon 120 110 100 Phon 100 90 Phon 90 80 Phon 80 70 70 Phon 60 Phon 60 50 Phon 50 Hz: 50dB50 40 Phon 40 30 Phon 30 20 Phon Sound pressure level (dB) level Sound pressure 20 10 Phon 10 1 kHz: 10dB 0 Frequency (Hz) 50 100 200 500 1k 2k 5k 10k 20k

The decibel scale - 11 VCE Physics.com Projectile motion - 12 VCE Physics.com