3. Draw diagrams to show the first three modes of resonance in the following instruments (also find the frequencies of these modes if the air temperature 20 C):

a) A clarinet 75 cm long that functions acoustically like a closed air column. b) An organ pipe open at both ends that is 4.8 m long.

c) A guitar string 1.3 m long with a wave speed of 66 m/s.

4. A guitar player is deliberately trying to produce beats by bending one string to make it almost match another unbent string's pitch. If the unbent string's frequency is 343 Hz andhe wants to hear nine beats in 2 s, what pitch(es) could he bend the string to?

5. Give an example of how music involves some aspects of subjectivity or individual perception, which can't be adequately described or explained by physics.