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.

The temperature in gavin's oven is a sinusoidal function of time. gavin sets his oven so that it has a maximum temperature of 280°f and a minimum temperature of 240°. once the temperature hits 280°, it takes 20 minutes before it is 280° again. gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 270°. he puts the cake into the oven when it is at 260° and rising. how long will gavin need to leave the cake in the oven? (round your answer to the nearest minute.)